A fast universal self-tuned sampler within Gibbs sampling

Bayesian inference often requires efficient numerical approximation algorithms, such as sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC) methods. The Gibbs sampler is a well-known MCMC technique, widely applied in many signal processing problems. Drawing samples from univariate fullconditional distributions efficiently is essential for the practical application of the Gibbs sampler. In this work, we present a simple, self-tuned and extremely efficient MCMC algorithm which produces virtually independent samples from these univariate target densities. The proposal density used is self-tuned and tailored to the specific target, but it is not adaptive. Instead, the proposal is adjusted during an initial optimization stage, following a simple and extremely effective procedure. Hence, we have named the newly proposed approach as FUSS (Fast Universal Self-tuned Sampler), as it can be used to sample from any bounded univariate distribution and also from any bounded multi-variate distribution, either directly or by embedding it within a Gibbs sampler. Numerical experiments, on several synthetic data sets (including a challenging parameter estimation problem in a chaotic system) and a high-dimensional financial signal processing problem, show its good performance in terms of speed and estimation accuracy. (C) 2015 Elsevier Inc. All rights reserved.